I used a 22-250 for a rifle hunt in texas and when we skinned that deer one of the shoulders was completely destroyed, so we couldn't get any meat of it. The other shoulder had bruised spots too so yea a 22-250 is plenty enough for deer.
Well the Texas deer that i have seen are no bigger than a large dog, so sure a 22-250 will work fine. Most people shoot deer in the 200lbs plus range though and a 22-250 is just too light to be effective in the hands of anyone short of marksmen at very short range. Killing should be merciful. Save the 22 calibers for the crows and coyotes please.
My personal preference for deer and hogs would be a 25-06, but there are many options that fit the bill